Adaptive signal processing systems have many applications including radar reception, cellular telephones, communications systems, and biomedical imaging. Adaptive signal processing systems utilize adaptive filtering to differentiate between the desired signal and noise. An adaptive filter is defined by four aspects: the type of signals being processed, the structure that defines how the output signal of the filter is computed from its input signal, the parameters within this structure that can be iteratively changed to alter the filter's input-output relationship, and the adaptive algorithm that describes how the parameters are adjusted from one time instant to the next.
Common applications of adaptive signal processing include: an adaptive radar reception antenna array, an adaptive antenna array for adaptive communications, and adaptive sonar. In these systems, desired signal detection and estimation is hindered by noise and interference. Interference may be intentional jamming and or unintentional received radiation. These antenna arrays may change their reception patterns automatically in response to the signal environment in a way that optimizes the signal power to interference power plus noise power ratio (abbreviated as SINR). The array pattern is easily controlled by weighting the amplitude and phase of the signal from each element before combining (adding) the signals. Adaptive arrays are especially useful to protect radar and communication systems from interference when the directions of the interference are unknown or changing while attempting to receive a desired signal of known form. Adaptive arrays are capable of operating even when the antenna elements have arbitrary patterns, polarizations, and spacings. This feature is especially advantageous when an antenna array operates on an irregularly shaped surface such as an aircraft or ship.
Adaptive signal processing systems are required to filter out undesirable noise. Due to the lack of a priori knowledge of an external environment, adaptive signal processing systems require a certain amount of statistically independent weight training data samples to effectively estimate the input noise covariance matrix. The input noise covariance matrix is the set of second central moments (i.e., moments about the mean) among the received antenna element voltages.
“Ideal” weight training data has a Gaussian probability distribution for both its real and imaginary baseband components. FIG. 1 is a frequency vs. amplitude plot representing an ideal Gaussian noise source with a bell-shaped probability curve in which the mean value is identical to the median value. However, real-world weight training data may be contaminated by undesirable impulse noise outliers, resulting in a non-Gaussian distribution of real and imaginary components.
The number of weight training data samples required for signal power to interference power plus noise power ratio (SINR) performance of the adaptive processor to be within 3 dB of the optimum on average is called the convergence measure of effectiveness (MOE) of the processor. A signal is stationary if its statistical probability distribution is independent of time. For the pure statistically stationary Gaussian noise case, the convergence MOE of the conventional Sample Matrix Inversion (SMI) adaptive linear technique can be attained using approximately 2N samples for adaptive weight estimation, regardless of the input noise covariance matrix, where N is the number of degrees of freedom in the processor (i.e., the number of antenna elements or subarrays) for a spatially adaptive array processor, or N is the number of space-time channels in a space-time adaptive processing (STAP) processor). Referred to as the SMI convergence MOE, convergence within 3 dB of the optimum using approximately 2N samples for adaptive weight estimation has become the benchmark used to assess convergence rates of adaptive processors. General information regarding SMI convergence MOE may be found in Reed, I. S., Mallet, J. D., Brennan, L. E., “Rapid Convergence Rate in Adaptive Arrays”, IEEE Trans. Aerospace and Electronic Systems, Vol. AES-10, No. 6, November, 1974, pp. 853-863, the disclosure of which is incorporated herein by reference.
Conventional sample matrix inversion (SMI) adaptive signal processing systems are capable of meeting this benchmark for the pure statistically stationary Gaussian noise case. If, however, the weight training data contains non-Gaussian noise outliers, the convergence MOE of the system increases to require an unworkably large number of weight training data samples. The performance degradation of the SMI algorithm in the presence of non-Gaussian distributions (outliers) can be attributed to the highly sensitive nature of input noise covariance matrix estimates to even small amounts of impulsive non-Gaussian noise that may be corrupting the dominant Gaussian noise distribution. General information regarding the sensitivity of the SMI algorithm may be found in Antonik, P. Schuman, H. Melvin, W., Wicks, M., “Implementation of Knowledge-Based Control for Space-Time Adaptive Processing”, IEEE Radar 97 Conference, 14-16 Oct., 1997, p. 478-482, the disclosure of which is incorporated herein by reference.
Thus, for contaminated weight training data, convergence rate slows significantly with conventional systems. Fast convergence rates are important for several practical reasons including limited amounts of weight training data due to non-stationary noise and computational complexity involved in generating adaptive weights. In other words, the time which elapses while a conventional system is acquiring weight training data and generating adaptive weights may exceed the duration of a given non-stationary noise environment, and an adaptive weight thus generated has become obsolete prior to completion of its computation.
Most real world data does not have a purely Gaussian probability distribution due to contamination by non-Gaussian outliers. Conventional signal processors assume that the weight training data has a Gaussian distribution, and therefore they do not perform as well as theory would predict when operating with real world data. If weight training data contains desired signals that appear to be outliers, the performance is similarly degraded. In an effort to compensate for these performance problems, conventional systems employ subjective data screening techniques to remove perceived outliers from the data prior to processing. However, subjective screening is undesirable because the process is ad-hoc in nature, requires many extra processing steps, and may even degrade system performance.
It would therefore be desirable to provide an adaptive signal processing system that accommodates outlier contaminated weight training data and still produces a convergence MOE which is comparable to the above referenced benchmark for SMI systems. It would also be desirable to provide a system that significantly reduces desired signal cancellation when weight training data includes desired signal components. See generally Gerlach, K., Kretschmer, F. F., Jr., “Convergence Properties of Gram-Schmidt and SMI Adaptive Algorithms, Part II”, IEEE Trans. Aerospace and Electronics Systems, Vol. 27, No. 1, January 1991, pp. 83-91, the disclosure of which is incorporated herein by reference.